In the final section we classify all irreducible \(\mathfrak {L}_{S, n} (B)\) -modules with non-uniformly bounded but finite dimensional weight spaces. The case \(n =1\)  follows from [1]} and [2]} with modest generalisations. For \(n \ge 2\) , we define a highest weight \(\mathfrak {L}_{S,n}(B)\) -modules for a given
triangular decomposition. Then by utilising results and techniques of [3]}, we prove in Theorem REF  that every irreducible \(\mathfrak {L}_{S,n}(B)\) -module with non-uniformly bounded but finite dimensional weight spaces is a highest module with an appropriate triangular decomposition. In Theorem REF 
we prove that the irreducible highest weight \(\mathfrak {L}_{S,n}(B)\) -modules with finite dimensional weight spaces are single point evaluation modules. This result relies on the fact that the highest weight space of highest weight module with finite dimensional weight spaces is an irreducible uniformly bounded
module for the lower rank Lie subalgebra which is a single point evaluation module by Theorem REF . Finally, just like in the uniformly bounded case, we prove that the finite dimensional abelian Lie algebra \(S\)  can be reduced to at most one dimension (Theorem REF ). The following is our main result:
